There are three points P, Q and R on a straight line such that PQ: QR = 3: 5. If n is the number of possible values of PQ: PR, then what is n equal to?
Answer & explanation
Answer: (b) 2
With PQ = 3 and QR = 5, either Q lies between P and R (PR = 8) or P lies between Q and R (PR = 2); R cannot lie between P and Q because QR is longer than PQ. That gives two ratios, 3 : 8 and 3 : 2.
- Take PQ = 3 and QR = 5 units.
- Q between P and R: PR = 3 + 5 = 8, so PQ : PR = 3 : 8.
- P between Q and R: QR = QP + PR, so PR = 5 − 3 = 2, giving PQ : PR = 3 : 2.
- R between P and Q is impossible: then QR (5) would be part of PQ (3).
- So there are 2 possible values: n = 2.
Remember · For points on a line, try each point as the middle one and drop the orders that break the given lengths.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·